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Full text of "Study of shape and internal structure of moon, utilizing lunar orbiter data quarterly progress report"

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6TH QUARTERLY PROGRESS REPORT 
Contract No. NSR 05-264-002 
January 1968 



STUDY OF SHAPE AND INTERNAL STRUCTURE 
OF MOON J 
UTILIZING LUNAR ORBITER DATA 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
LUNAR ORBITER PROGRAM OFFICE 

Prepared by 

Donald L, Laiaar 

and 

J. ¥, McGann- Lamar 

EARTH SCIENCE RESEARCH CORPORATION 

P.O. Box 5427 

Santa Monica ^ California 90405 

Area Coda 213 - 395-4528 



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smmRY 

Detenninatlons of the luimr radius with respect to the center of 
mass are inconsistent with elevations shown on the AGIC lunar charts. 
These discrepancies may be the result of a displacement of the moon's 
center of volume and center of mass. This displacement may be related 
to a systematic excess in elevation of continents over marla» Analysis 
of the relationship betx^een the moon's shape, gravity field ^ and in- 
ternal structure requires knowledge of the coordinates of the center 
of figure with respect to the center of mass. 



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RELATIVE ELE¥ATION OF CONTINENTS AMD MARIA 

Determinations of the lunar radius by analysis of ranger Impacts 
(Sjogren and Trask, 1965), image motion study of Lunar Orbiter photo- 
graphs (Michael, 1967), and radar observations (Shapiro^ ^ £i» 1967) 
have yielded values which are inconsistent with the elevations shown 
on the ACIC charts. The origin of coordinates for the charts is a 
mean sphere which best fits the center of volume and the origin for 
the other determinations is the center of mass. Thus it has been sug- 
gested (Michael, 1967; Shapiro, £t al, 1967), that the discrepancies 
may be the result of displacement between the moon's center of figure 
and center of mass. The relationship between the center of figure and 
center of mass must be known to accurately determine the relationship 
between the gravity field, shape and internal structure. Eventually 
it will be desirable to prepare contour maps with elevations given 
with respect to the moon's center of mass. With present knowledge it 
may be possible to approximate the moon's gross shape on the assump- 
tion of a systematic difference In elevation between continents and 
maria. Munk and MacDonald (1960) followed a similar approach by as- 
suming a systematic difference in elevation between continents and 
ocean basisas in their analysis of the relationship between the earth's 
shape, gravity field and Internal structure. 

It was previously suggested (Lamar and McGann» 1966a) that the 
average elevation (relative to the center of mass) of the continents 
is 3 kin greater than the maria. Goudas (1966) questioned this assump- 
tion and pointed out that recent stereoscopic height determinations 
reveal no such relationship. The origin of coordinates for these sys- 
tems is a mean sphere which best fits the points or the center of 
volume. Thus the relationship between the center of volume and center 
of figure must be known before any systematic difference in elevation 
between continents and maria can be established from the stereoscopic 
observations. 

The problem may be visualized by imagining that the earth lacks 
oceans, which provide a convenient level surface centered on the earth's 



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ceiiter of mass. An observer on the moon studying the earth's shape 
by stereoscopic methods or observations of the limb would logically 
choose the earth's center of volume as the origin of coordinates. If 
our lunar observer viewed the earth with the center of the Pacific 
basin on one limb, the center of the Pacific basin would have about 
the same elevation as continental areas on the earth* s opposite side, 
relative to a coordinate system with its origin at the center of the 
earth's disk or center of volume. Similarly in the case of the moon 
it is possible that the continents are systematically higher relative 
to the center of mass and that some maria surfaces relative to the 
center of figure are higher than some continental areas. Therefore 
it is not possible to use the stereoscopic height determinations to 
establish any systematic moon-wide difference in elevation bett^een 
continents and maria until such observations are transformed so that 
the origin of coordinates is the center of mass. Thus the authors 
(Lamar and McGann, 1966a, b) were incorrect in stating that Hedervari's 
analysis of Baldwin's (1961^ 1963) data waa pertinent nor does the 
relative accuracy of the stereoscopic determinations by different in- 
vestigators discussed by Goudas (1966) have any bearing on the problem. 

As shown in Fig, 1, if a systematic difference in elevation, 
amounting to H, exists between continents and maria on opposite hemi- 
spheres then the displacement between the center of mass and center of 
figure is H/2. According to O'Keefe and Cameron (1962) on the moon's 
earth facing hemisphere the displacement is about 1 kai^ the center of 
figure lying south of the center of mass. This is consistent with the 
higher percentage of continental areas in the moon's southern hemi- 
sphere and a systematic difference in elevation of about 3 km. 

Analysis of tracking data from the Ranger flights to the moon 
(Sjogren and Trask, 1965) and the first photographs (U.S.S.R. Academy 
of Sciences, 1960) of the moon's farside provided the first indication 
that an analogous relationship exists between the moon's farside and 
earth-facing hemispheres. The farsida pictures indicate that there 
is a much smaller percentage of maria on the farside relative to the 
hemisphere facing the earth. Thus if a systematic difference in ele- 
vation between continents and maria exists ^ the moon's center of figure 



MARIA 




CONTINENT 



Fig. 1 Diagram indicating relationship between center of mass (c. m.) and 
center of figure (c. f.) for concentration of maria and contiaents 
In distinct hemispheres « A systematic excess in. elevation (H) of 
continettts over maria with respect to a level surface is assumed. 



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relative to the center of mass should be displaced away from the earth 
(Fig. 1). Tracking of the Ranger spacecraft revealed that the radius 
from the center of mass is about 3 km less than the value indicated on 
the ACIC charts (Sjogren and Trask^ 1965), As the origin of coordinates 
for these charts is based on a mean sphere determined from stereoscopic 
observations, the Ranger data indicate that the center of figure is 
displaced away from the earth. This displacement could have been pre- 
dicted from the relative absence of maria on the farside and the as- 
suinption of a systematic excess in elevation of the continents over 
the maria. 

Preliminary determinations of the moon's radius with respect to 
the center of mass in the equatiroal region facing the earth have been 
accomplished by analysis of image motion on pictures taken by Lunar 
Orbiter (Michael^ 1967) « This investigation also reveals that the 
radii are systematically lower by 1 to 3 km (average about 2 km) than 
the radii on the curve obtained from harmonic analysis of the ACIC 
selenodetic control system by Bray and Goudae (1966). Measurements 
of the lunar radius by combining radar determinations of the distance 
to sub-earth points on the moon and range data of Lunar Orbiter 1 and 
2 also produced values about 1 to 2 km less than the radii determined 
from the stereoscopic observations (Shapiro^ ®t al ^ 1967). 

Thus the analysis of data from the Lunar Orbiters substantiates 
the hypothesis of a systematic excess of elevation of continental areas 
over maria which is related to a displacement of the center of figure 
from the center of mass. However, the displacement of about 2 km be- 
tween the earthward and farside hemispheres (corresponding to H/2 on 
Fig. 1) leads to an unexpectedly high estimate of about 5 km for the 
excess in elevation of continents over maria (H on ¥±g. 1). It should 
be aoted that the radii determinations by image motion are concentrated 
in the equatorial region (Michael, 1967) which Is predominaately maria i 
thug the relative percentage of maria on the earthward side may be 
overemphasized. Although additional studies of the shape of the moon 
are required to verify the existence and magnitude of a systematic ex- 
cess in elevation of continants over maria ^ the existing data appear to 
eliminate the possibility that maria are higher than continents. 



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REFERENCES 



Baldwin, R. B, (1961) A lunar contour map; Sky and Telescope , Vol. 21, 
pp. 84-85. 

Baldwin^ R. B, (1963) The Measure of the Moon ; Univ. of Chicago Press, 
Chicago, Illinois , 488 pp. 

Bray, T. A. and C. L. Goudas (1966) A contour map based on the seleno- 
datic control system of the A.C.I.C.; Icarus , Vol. 5^ pp. 526-535. 

Goudas, C. L. (1966) Note on "Shape and internal structure of the moon" 
by Lamar and McGann; Icarus , Vol, 5, pp. 99-100. 

Lamar, D. L. and Jeaimlne McGann (1966a) Shape and internal structure 
of the moon; Icarus ^ Vol. 5, pp. 10-23. 

Lamar, D. L. and Jaannine McGann (1966b) Reply to "Note on the shape 
and internal structure of the moon" by C. L. Goudas; Icarus , Vol. 5, 
p. 101. 

Michael, W. H. , Jr. (1967) Physical properties of the moon as determined 
from Lunar Orbiter data; Presented at the Fourteenth General Assembly 
of the International Union of Geodesy and Geophysics Meetings Lucerne ^ 
Switzerland. 13 pp. 

Munks W. H. and G, J. F. MacDonald (1960) Continental! ty and the gravi- 
tational field of the earth; J. Geophys. Res., Vol. 65, pp. 2169-2172, 

O'Keefes J« A. and W. S. Cameron (1962) Evidence from the moon's surface 
features for the production of lunar granites; Icarua , Vol. 1, pp. 
271-285, 

Shapiro, A,, E. A. Uliana, B. S. Yaplee, and S. H. Knowles (1967) Lunar 
radius from radar measurements; Presented at COSPAS. Assembly, London, 
England s 23 pp. 

Sjogren, W. L. and D. W. Trask (1965) Results on physical constants and 
related data from the radio tracking of Mariner (Venus) and Ranger 
III-VII missions; J. Spacecraft ; Vol. 2, pp. 689-697. 

U.S.S.R., Academy of Sciences (1960) The other aide of the moon, trans- 
lated by J. B. Sykes; Pergamon^ New Yorkj 36 pp.